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Comparative performance study of QN and LM algorithms in predictive control for NNARX-identified model of hydro-power plant

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An Erratum to this article was published on 02 February 2007

Abstract

In this paper input-constrained predictive control strategy for NNARX (neural network non-linear auto-regression with exogenous signal) model of hydro-turbine is presented. The input (gate position) and output (turbine power) data are generated by means of dynamic plant model. The collected data are utilized to develop the NNARX model of the plant. Then NN-based predictive control (NNPC) scheme is applied to control the turbine power. The control cost function (CCF) includes the squared difference between the model predicted output and desired response and a weighted squared change in the control signal. The CCF is minimized with both Quasi-Newton and Levenberg–Marquardt iterative algorithms. To demonstrate the suitability of the strategy, the plant has been simulated on two different reference signals.

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Abbreviations

\(\bar{H}_{\rm surge}, \bar{H}_{\rm turbine}\) :

head available in riser of surge tank, turbine (p.u.)

\(\bar{H}_{\rm tunnel}, \bar{H}_{\rm penstock}\) :

head loss in tunnel, penstock (p.u.)

\(\bar{U}_{\rm tunnel}, \bar{U}_{\rm turbine}, \bar{U}_{\rm surge}\) :

velocity of water in tunnel, turbine, surge tank (p.u.)

\(\bar{U}_{\rm noload}\) :

velocity of water at no load (p.u.)

f tunnel, f penstock :

head loss coefficient in tunnel, penstock (p.u.)

C surge :

storage constant of surge tank (s)

\(\bar{H}_{{\rm devia},{\rm tunnel}} \) :

head deviation in tunnel (p.u.)

\(\bar{H}_{{\rm devia},{\rm penstock}} \) :

head deviation in penstock (p.u.)

Z p :

hydraulic surge impedance of penstock (=T w/T ep)

T w :

water time constant in penstock (s) \({({= LU_{0}/gH_{0}})},\) T w varies with load

T ep :

elastic time constant of penstock (s)

T wc :

water time constant in tunnel (s)

L :

length of penstock

U 0 :

velocity of water in penstock at rated head (p.u.)

g :

acceleration due to gravity

H 0 :

rated turbine head (p.u.)

\(\Delta \bar{\omega}\) :

deviation of rotor speed (p.u.)

\(\bar{G}_{\rm opening} \) :

gate opening (p.u.)

D turbine :

damping factor or coefficient in p.u. torque/p.u. speed deviation

A gain :

turbine gain

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Authors and Affiliations

  1. Department of Electrical Engineering, Motilal Nehru National Institute of Technology, Allahabad, India

    S. P. Singh

  2. Department of Electrical Engineering, Royal Bhutan Institute of Technology, Phuentsholing, Bhutan

    Nand Kishor, A. S. Raghuvanshi & P. R. Sharma

Authors
  1. Nand Kishor
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  2. S. P. Singh
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  3. A. S. Raghuvanshi
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  4. P. R. Sharma
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Correspondence to Nand Kishor.

Additional information

An erratum to this article can be found at http://dx.doi.org/10.1007/s00366-007-0055-0

Appendix

Appendix

Parameters of the system studied:

Z p (T w/T ep)=6.335; T w=2.23 s; T ep=0.352 s; T wc=39.15 s; C surge=240 s; f tunnel=0.0475 p.u.; f penstock=0.089 p.u.; A gain=1.67; \(\bar{U}_{\rm noload} = 0.13\,\hbox{p.u.};\) Δ ω=0.05; D turbine=2.0.

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Kishor, N., Singh, S.P., Raghuvanshi, A.S. et al. Comparative performance study of QN and LM algorithms in predictive control for NNARX-identified model of hydro-power plant. Engineering with Computers 23, 71–78 (2007). https://doi.org/10.1007/s00366-006-0024-z

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